Having suggested that there can be a scale of evaluation for “acts or occasions of intellection” in much the same way as there can be a scale of evaluation for poems, given an “investigation” in which intellection or poeisis is engaged and a “problem space” which it explores, I now want to consider what it might mean to speak of equality in the context of an egalitarian political maxim.

In set theory, two sets are equal if they are included in each other, in other words if everything that is in set a is in set b and vice versa. Equality here is identity: if a=b, then the names a and b name the same set. Given two sets a and b, we can always tell whether they are equal or not. But their inequality means nothing other than their non-identity, the fact that they are differently composed. If a is not equal to b, that is because there is some c that either belongs to a without belonging to b or belongs to b without belonging to a.

The difference between a and b actually makes up a set of its own: it is the set made by taking the union of a and b and subtracting their intersection. In the set theoretical universe, differences have the same sort of contexture, the same sort of mathematical reality, as the entities between which differences arise. My blue hat and your club foot can be composed together to form a kind of chimera, a set taken from our mutually differentiating features, to which both of us have contributed and yet neither of us is equal. This is the positive form taken by sexual difference: a chaotic admixture of sexual traits that does not form a sexual being (it is not a hermaphrodite, since the intersection of masculine and feminine is subtracted from it). Is it not this compound semi-entity, the “beast with two backs”, that pornography displays?

It is clear that when we speak of political equality, we are not speaking of ontological non-difference. Might we instead be speaking of equivalence, equal-valuedness? For equivalence to arise, there must be a scale of values, a relation over the domain to be evaluated. Equivalence is reflexive: I am equal-valued to myself. It is transitive: my equal-valuedness to you entails my equal-valuedness to everyone to whom you are equal-valued. It is symmetrical: my equal-valuedness to you entails your equal-valuedness to me. It is not, however, global: I may have no relation to you whatsoever, you and I may participate in entirely discrete equivalences. We can derive from this the schema of a familiar caricature of multiculturalism: discrete communities, characterised by the immediate substitutibility of any one member of a community for another of the same community, with no relation of rank between them.

Equality - political equality, which is proposed by an egalitarian maxim such as “all are created equal” - is neither identity nor a relation. What then can it be? The answer I think is that equality is the choice between a saturated relation (a relation in which every element in the domain is related to every other element) and non-relation, sustained by the prohibition of any inegalitarian proposition. Now, a relation over a domain is simply a subset of the Cartesian product of that domain with itself (e.g. {a, b, c}^2 = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c)…}). The subset is obtained by separating those pairs of elements that are in the relation out of the set of all possible pairs; and the pairs to be separated are identified by a predicate. A maxim such as “all are created equal” essentially declares that any such separation is illegitimate: either all are related in the same way (“all men are brothers”) or there is no relation at all. Any predicate that would identify some pairs of elements as being in relation and others as not is forbidden.

In a saturated relation (“all men are brothers”), the Cartesian product of the domain with itself produces a simple and uniform verification of the domain’s original consistency: it is a kind of formal re-registering of the univocity of the count (“being is said in the same way of everything of which it is said”, and this saying is reiterated in the innocent combinatorial reduplication of the self-product). The maxim effectively declares that the consistency of the domain is borne out by this restatement, and that any predicative separation, distinguishing between those elements that are paired and those that are not, would bring the ontological integrity of the original set into question. If all men are not brothers, then the sense of “man” is equivocal, two-faced: what is he if he can be a brother to some of his fellows but not to others?

Neither poems nor instances of intellection are subject to any egalitarian rubric, because neither are required to affirm that the material of which they are composed is univocally consistent. An egalitarian maxim asserts, in effect, that the political subject it announces is real, that it is not a chimera. For poetry and thought, on the contrary, it is a matter of hazarding the consistency of what at first appears to be chimerical, the insistence of a singularity.